A student, by mistake, wrote 64 instead of 46 as one of the numbers while finding the average of 10 given numbers, and obtained the average as 50. What is the correct average of the 10 numbers after adjusting this mistake?

Introduction / Context:
This question involves correcting an average when one of the numbers used in the calculation was wrong. Understanding how a single error affects the overall average is important in data interpretation and basic statistics.

Given Data / Assumptions:
• Number of values = 10.• Incorrect number used in the calculation = 64.• Correct number should have been = 46.• Average obtained using the wrong number = 50.• All other values are correctly recorded.

Concept / Approach:
The average of a group of numbers is the total sum divided by the number of numbers. When one number is incorrect, the total is off by the difference between the wrong and correct values. After adjusting the total, you divide by the same count to get the corrected average.

Step-by-Step Solution:
Step 1: Let S be the total sum based on the incorrect data.Step 2: Since the average with the mistake is 50, S = 10 * 50 = 500.Step 3: The incorrect value is 64 and the correct value is 46.Step 4: Correct total sum = S - incorrect value + correct value = 500 - 64 + 46.Step 5: Compute 500 - 64 = 436, then 436 + 46 = 482.Step 6: Correct average = corrected total sum / number of values = 482 / 10.Step 7: 482 / 10 = 48.2.

Verification / Alternative check:
The difference between the correct and incorrect value is 46 - 64 = -18. This means the true total is 18 less than the original total. The average must therefore decrease by 18 / 10 = 1.8. Subtracting 1.8 from the incorrect average of 50 gives 48.2, confirming our calculation.

Why Other Options Are Wrong:
48: This would correspond to a total change of 20 instead of 18.48.1: This is slightly low and reflects incorrect handling of the decimal change.49: This is too high and does not account fully for the reduced total after correction.

Common Pitfalls:
Many students forget to adjust the sum by both removing the incorrect entry and adding the correct one. Others may incorrectly divide the difference or misplace the decimal point. Carefully tracking the change in total and dividing by the correct number of observations is essential.

Final Answer:
The correct average of the 10 numbers is 48.2.